An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Zanna, L. Del; Bucciantini, N.; Londrillo, P.

doi:10.1051/0004-6361:20020776

Cited by 220 publications

(305 citation statements)

References 31 publications

(33 reference statements)

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“…The dashed red line in Fig. 10 shows the growth rate for PLUTO with the third order convex-eno reconstruction (Del Zanna & Bucciantini 2002). The growth rate is closer to γ MRI for the doubled resolution (green lines).…”

Section: Initial 4 Mode Perturbationmentioning

confidence: 84%

High-order Godunov schemes for global 3D MHD simulations of accretion disks

Flock¹,

Dzyurkevich²,

Klahr³

et al. 2010

A&A

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We assess the suitability of various numerical MHD algorithms for astrophysical accretion disk simulations with the PLUTO code. The well-studied linear growth of the magneto-rotational instability is used as the benchmark test for a comparison between the implementations within PLUTO and against the ZeusMP code. The results demonstrate the importance of using an upwind reconstruction of the electro-motive force (EMF) in the context of a constrained transport scheme, which is consistent with plane-parallel, grid-aligned flows. In contrast, constructing the EMF from the simple average of the Godunov fluxes leads to a numerical instability and the unphysical growth of the magnetic energy. We compare the results from 3D global calculations using different MHD methods against the analytical solution for the linear growth of the MRI, and discuss the effect of numerical dissipation. The comparison identifies a robust and accurate code configuration that is vital for realistic modeling of accretion disk processes.

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Section: Initial 4 Mode Perturbationmentioning

confidence: 84%

High-order Godunov schemes for global 3D MHD simulations of accretion disks

Flock¹,

Dzyurkevich²,

Klahr³

et al. 2010

A&A

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“…As mentioned already, it is based on the so-called central scheme, which guarantees good accuracy even if the flows include strong shocks or high Lorentz factors. Magnetic fields can also be included ( Del Zanna & Bucciantini 2002;Shibata & Sekiguchi 2005;Duez et al 2005). …”

Section: Appendix General Relativistic Hydrodynamic Codementioning

confidence: 99%

General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole

Nagakura¹,

Yamada²

2008

Astrophysical Journal

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We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole using two-dimensional general relativistic hydrodynamic simulations, as well as linear analysis, in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to nonaxisymmetric perturbations. The results of the dynamical simulations show good agreement with the linear analysis on the stability and the oscillation and growth timescales. A comparison of different wave-travel times with the growth timescales of the instability suggests that it is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of the perturbations are too long to allow a clear definition of the reflection point. By analyzing the nonlinear phase in the dynamical simulations, we show that quadratic mode couplings precede the nonlinear saturation. It is also found that not only short-term random fluctuations due to turbulent motion, but also quasi-periodic oscillations on longer timescales, take place in the nonlinear phase. We give some possible implications of the instability for black hole quasi-periodic oscillations and the central engine in gamma-ray bursts.

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“…In the present paper we describe a novel code for GRMHD in dynamical spacetimes, named X-ECHO, aimed at studying the evolution of magnetized relativistic stars and the gravitational collapse of the magnetized rotating cores of massive stars. X-ECHO is built on top of the Eulerian conservative high-order code (Del Zanna et al 2007) for GRMHD in a given and stationary background metric (Cowling approximation), which in turn has upgraded the previous version for a Minkowskian spacetime (Del Zanna & Bucciantini 2002;Del Zanna et al 2003). ECHO relies on robust shock-capturing methods within a finite-difference discretization scheme (two-wave Riemann solvers and limited high-order reconstruction routines), with a staggered constrained-transport method used to preserve the divergence-free condition for the magnetic field (to machine accuracy for second order of spatial accuracy), as proposed by Londrillo & Del Zanna (2000, 2004.…”

Section: Introductionmentioning

confidence: 99%

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

Bucciantini

Zanna

2011

A&A

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109

136

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We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This aims at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as in the evolution of magnetized neutron stars or in the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code extends the Eulerian conservative high-order (ECHO) scheme (Del Zanna et al. 2007, A&A, 473, 11) for GRMHD, here coupled to a novel solver of the Einstein equations in the extended conformally flat condition (XCFC). We solve the equations in the 3 + 1 formalism, assuming axisymmetry and adopting spherical coordinates for the conformal background metric. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and are solved, for each harmonic, by inverting band diagonal matrices. As a side product, we built and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.

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An efficient shock-capturing central-type scheme for multidimensional relativistic flows

Cited by 220 publications

References 31 publications

High-order Godunov schemes for global 3D MHD simulations of accretion disks

High-order Godunov schemes for global 3D MHD simulations of accretion disks

General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

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